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Method of Finding HCF

If 'n' is any...

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If 'n' is any positive integer then by Euclid algorithm. Show that n can be expressed in the form of 3m or 3m+1 ; where 'm' is some integer.

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n

be any positive integer, then by using Euclid's division algorithm, show that
(i)

n^{3}

can be expressed in the form

9 m, 9 m + 1

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m

is some integer.

Q. Let Euclids division lemma to show that the square of any positive integer is either of the form

3 m

3 m + 1

for some integer

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x

be any positive integer then it is of the form

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3 q + 2

. Now square each of these and show that they can be rewritten in the form

3 m

3 m + 1

Q. Show that the square of any positive integer is of the form

3 m

3 m + 1

for some integer

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Q. Question 4
Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
[Hint: Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]

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Method of Finding HCF

Standard X Mathematics